Question

Which data set has the greatest spread for the middle 50% of its data?


{18, 13, 22, 17, 21, 24}



{17, 19, 22, 26, 17, 14}



{13, 17, 12, 21, 18, 20}



{18, 21, 16, 22, 24, 15}

Answer 1

You should find the middle 50% of the data for each set.

Answer 2

I figured that much on my own, why is the middle 50% though?

Answer 3

*what

Answer 4

There are 6 items in each set. 50% of 6 is 3.

Order the sets and pick the middle 3.

Answer 5

13,17,18,21,22,24
14,17,17,19, 22,26
12,13,17,18,20,21
15,16,18, 21,22,24

Answer 6

Nicely ordered. Now pick the middle three from each.

Answer 7

they each have 6 numbers, there isn't a middle three, two of them are in the middle

Answer 8

@nincompoop

Answer 9

@Hero

Answer 10

Well, you must decide if you will take 2 or 4. Which actually contains the middle 50%? It is a common problem with small datasets.

Answer 11

so the middles would be 18, 21
17,19
17,18 and 18, 21

Answer 12

That does not contain 50%.

Answer 13

huh?

Answer 14

You must use AT LEAST 50% of the data. Picking the middle 2 is only 1/3 of the data. You'll have to go up to 2/3.

Answer 15

okay so the middle two are 21,22
19,22
18,20
and 21,22

Answer 16

... and that is not helpful because you are examining only the middle 1/3. You need 1/2 AT LEAST.

Answer 17

shouty capitals are not helpful, so what you mean is I need at least half of those numbers to examine?

Answer 18

It's not shouty. It's just emphasis.

Perhaps a different approach. Can you find the median of each dataset?

Answer 19

that I can do

Answer 20

Do you get 21.5, 20, 19, and 21.5?

Answer 21

yes

Answer 22

Okay, how about the medians of the two subsets created by those medians?

In other words, given {18, 13, 22, 17, 21, 24}

Sorted: 13, 17,18, 21, 22, 24
Median: 19.5
Left subset: 13 17 18 ==> Median 17
Right subset 21 22 24 ==> Median 22

Make any sense?

Answer 23

makes sense

Answer 24

Well, what we have just created is this list:

25th percentile = 17
50th percentile = 19.5 = Median
75th percentile = 22

Comparing the 75th to the 25th creates the "Interquartile Range". Notice how 75% - 25% = 50%. Thus, it is possible that the "middle 50% of the data" simply means the interquartile range.

22 - 17 = 5

Is this greater than or less than the interquartile range of the other sets?

Answer 25

greater than

Answer 26

I believe you, but I have not calculated them. The difficulty is what is meant by "middle 50% of the data". Originally, I was interpreting that literally and it was confusing. When I decided it might just mean the Interquartile Range, we had something that could be understood and solved.

Answer 27

so which set has the greatest spread

Answer 28

You tell me. Which has the greatest interquartile range? I did the first set.

Answer 29

I think its b